Pepona M, Shek A C M, Semprebon C, Krüger T, Kusumaatmaja H
Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom.
Smart Materials and Surfaces Laboratory, Department of Mathematics, Physics and Electrical Engineering, Ellison Place, Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom.
Phys Rev E. 2021 Feb;103(2-1):022112. doi: 10.1103/PhysRevE.103.022112.
We present a thermodynamically consistent model of a ternary fluid interacting with elastic membranes. Following a free-energy modeling approach for the fluid phases, we derive the governing equations for the dynamics of the ternary fluid flow and membranes. We also provide the numerical framework for simulating such fluid-structure interaction problems. It is based on the lattice Boltzmann method for the ternary fluid (Eulerian description) and a finite difference representation of the membrane (Lagrangian description). The ternary fluid and membrane solvers are coupled through the immersed boundary method. For validation purposes, we consider the relaxation dynamics of a two-dimensional elastic capsule placed at a fluid-fluid interface. The capsule shapes, resulting from the balance of surface tension and elastic forces, are compared with equilibrium numerical solutions obtained by surface evolver. Furthermore, the Galilean invariance of the proposed model is proven. The proposed approach is versatile, allowing for the simulation of a wide range of geometries. To demonstrate this, we address the problem of a capillary bridge formed between two deformable capsules.
